Development and application of mathematical and statistical methods for the genetic analysis of complex human traits is proposed. In particular, the primary focus is on developing methods for understanding complex patterns of inheritance through genetic linkage markers. The advent of restriction fragment length polymorphisms (RFLP's) spanning the entire genome now offers the power to achieve such analysis. Specifically, we intend to: elaborate models of inheritance involving multiple loci (for example, epistasis and genetic heterogeneity model); determine the power of detecting linkage for such complex models; determine the ability to establish complex patterns of inheritance with multiple linked markers. We will also examine variable age of onset as a potential indicator of genetic heterogeneity, and its impact on a linkage analysis. Finally, we will examine the application of linkage analysis for multivariate traits, and determine the power of linkage to explain genetic sources of correlation among traits. The methods that are developed will be applied to three major data sets. First, multivariate data including family history on idiopathic torsion dystonia will be examined with the goal of establishing genetic heterogeneity; this will have important ramifications for proposed family and linkage studies. Second, a large sample of family data on breast cancer (4700 probands) will be examined to determine the possibility of genetic heterogeneity as determined by age of onset and possibly other risk factors; these results will impact on linkage analyses of breast cancer. Third, an extensive set of data on immune response to twelve pneumococcal antigens and HLA, Gm and Km in South American Indian families will be analyzed from a multivariate-genetic standpoint to determine genetic patterns of correlation. The role of HLA, Gm and Km in the familial patterns will be determined. It is anticipated that the methods developed will have broad applicability beyond the specific projects described above. The results of this project will be of significant clinical and public health importance because they will offer a better understanding of disease etiology and the (possibly complex) genetic contribution to it, as well as provide avenues for treatment design, prevention, and accurate risk assessment.